1. Field of the Invention
This invention relates to methods and apparatus for optical sensing, including counting and sizing of individual particles of varying size in a fluid suspension, and more particularly, to such methods and apparatus which yield higher sensitivity and coincidence concentration than can be realized by optical sensors of conventional design.
2. Description of Related Art
It is useful to review the principles underlying the traditional method of optical particle counting, hereinafter referred to as single-particle optical sensing (SPOS). Sensors that are used to implement SPOS are based on the physical technique of light extinction (LE) or light scattering (LS), or some combination of the two. The optical design of a traditional SPOS sensor based on the LE technique is shown schematically in FIG. 1. A fluid, consisting of a gas or liquid, in which particles of various sizes are suspended, is caused to flow through a physical flow channel 10, typically of rectangular cross section. Two of the opposing parallel surfaces 12 and 14 defining the flow channel are opaque, while the remaining two opposing parallel surfaces 16 and 18 perpendicular to the opaque pair are transparent, comprising the “front” and “back” windows of the flow cell 10. A beam of light 20 of appropriate shape enters front window 16 of flow cell 10, passes through the flowing fluid and particles, exits flow cell 10 through back window 18 and impinges on a relatively distant light-extinction detector DLE.
The width of front and back windows 16 and 18 along the direction defined by the x-axis is defined as “a” (FIG. 1). The depth of flow cell 10, along the direction defined by the y-axis, parallel to the axis of the incident light beam, is defined as “b.” Suspended particles of interest are caused to pass through flow cell 10 along the direction defined by the z-axis (from top to bottom in FIG. 1) at a steady, appropriate rate of flow, F, expressed in units of milliliters (ml) per second, or minute.
The optical sensing zone 22 (“OSZ”), or “view volume,” of the sensor is the thin region of space defined by the four internal surfaces of flow channel 10 and the ribbon-like beam of light that traverses channel 10. The resulting shape of the OSZ resembles a thin, approximately rectangular slab (having concave upper and lower surfaces, as described below), with a minimum thickness defined as 2w, oriented normal to the longitudinal axis of flow cell 10 (FIG. 1). Source of illumination 24 is typically a laser diode, having either an elliptical- or circular-shaped beam, with a gaussian intensity profile along each of two mutually orthogonal axes and a maximum intensity at the center of the beam. Two optical elements are typically required to create the desired shape of the incident light beam that, together with the front and back windows of the flow channel 10, defines the OSZ. The first optical element is usually a lens 26, used to focus the starting collimated beam at the center (x–y plane) of flow cell 10. The focused beam “waist,” or width, 2w, is proportional to the focal length of the lens and inversely proportional to the width of the starting collimated beam, defined by its 1/e2 intensity values. The focused beam width, 2w, also depends on the orientation of the beam, if its cross section is not circular.
The second optical element is typically a cylindrical lens 28, used to “defocus,” and thereby widen, the light beam in one direction—i.e. along the x-axis. In effect, cylindrical lens 28 converts what otherwise would be a uniformly focused beam (of elliptical or circular cross section) impinging on the flow cell, into a focused “line-source” that intersects flow channel 10 parallel to the x-axis. The focal length and location of cylindrical lens 28 are chosen so that the resulting beam width (defined by its 1/e2 intensity points) along the x-axis at the center of the flow cell is much larger than the width, a, of the flow channel 10. As a result, front window 16 of the sensor captures only the top portion of the gaussian beam, where the intensity is nearly uniform. Substantial uniformity of the incident intensity across the width (x-axis) of the flow channel 10 is essential in order to achieve optimal sensor resolution. The intensity profile along the z-axis of the resulting ribbon-like light beam is also gaussian, being brightest at the center of the OSZ and falling to 1/e2 at its “upper” and “lower” edges/faces, where the distance between these intensity points defines the thickness, 2w, of the OSZ.
The shape of the OSZ 22 deviates from that of an idealized, rectangular slab shape suggested in FIG. 1. Rather, the cross-sectional shape of the OSZ in the y–z plane resembles a bow tie, or hourglass, owing to the fact that the incident light beam is focused along the y-axis. However, assuming that the optical design of the sensor has been optimized, the focal length of the focusing lens will be much larger than the depth, b, of the flow cell. Therefore, the “depth of field” of the focused beam—defined as the distance between the two points along the y-axis at which the beam thickness expands to √2×2w—will be significantly larger than the depth, b, of the flow cell. Consequently, the variation in light intensity will be minimal along the y-axis.
The ribbon-like light beam passes through the fluid-particle suspension and impinges on a suitable light detector DLE (typically a silicon photodiode). In the absence of a particle in the OSZ, detector DLE receives the maximum illumination. A particle that passes through the OSZ momentarily “blocks” a small fraction of the incident light impinging on detector DLE, causing a momentary decrease in the photocurrent output of detector DLE and the corresponding voltage “VLE ” produced by suitable signal-conditioning means. The resulting signal consists of a negative-going pulse 30 of height ΔVLE, superimposed on a d.c. “baseline” level 32 of relatively large magnitude, V0, shown schematically in FIG. 2. Obviously, the larger the particle, the larger the pulse height, ΔVLE, both in absolute magnitude and as a fraction of V0.
The detector signal, VLE, is processed by an electronic circuit 34, which effectively removes the baseline voltage, V0, typically either by subtracting a fixed d.c.voltage from VLE or by “a.c. coupling,” using an appropriate high-pass filter. This action allows for capture of the desired negative-going pulses of various heights, ΔVLE. The resulting signal pulses are then “conditioned” further, typically including inversion and amplification. Each pulse is digitized using a fast, high-resolution analog-to-digital (A/D) converter, allowing its height to be determined with relatively high accuracy. A calibration table is generated, using a series of “standard” particles (typically polystyrene latex spheres) of known diameter, d, spanning the desired size range. This set of discrete values of ΔVLE vs d is stored in computer memory and typically displayed as log ΔVLE vs log d, with a continuous curve connecting the points. The set of measured pulse heights, ΔVLE, are easily converted to a set of particle diameters, d, by interpolation of the calibration table values.
In principle, there are several physical mechanisms that can contribute to the light extinction effect. These include refraction, reflection, diffraction, scattering and absorbance. The mechanisms of refraction and reflection dominate the LE effect for particles significantly larger than the wavelength of the incident light, typically 0.6–0.9 micrometers (μm). In the case of refraction, the light rays incident on a particle are deflected toward or away from the axis of the beam, depending on whether the refractive index of the particle is larger or smaller, respectively, than the refractive index of the surrounding fluid. Provided the two refractive indices differ sufficiently and the (small) detector element, DLE, is located sufficiently far from the flow cell, the refracted rays of light will diverge sufficiently that they fail to impinge on detector DLE, thus yielding the desired signal, ΔVLE. The mechanism of reflection necessarily accompanies refraction, and the greater the refractive index “contrast” between the particles and fluid, the greater the fraction of incident light reflected by the particle. The phenomenon of diffraction typically has a negligible effect on the LE signal, because the angles associated with the major intensity maxima and minima are smaller than the typical solid angle defined by the distant detector DLE.
By contrast, however, the light scattering phenomenon typically makes an important contribution to the LE signal. It is the dominant mechanism for particles comparable in size to, or smaller than, the wavelength of the incident light. The magnitude and angular distribution of the scattered light intensity depends on the size, shape and orientation of the particle, as well as the contrast in refractive index and the wavelength of the beam. The well-known Mie and Rayleigh scattering theories describe in detail the behavior of the light scattering intensity. The greater the amount of light scattered off-axis, away from the axis of the incident light beam, the smaller the light flux that reaches the extinction detector DLE.
The mechanism of absorbance may be significant for particles that are highly pigmented, or colored. The magnitude of this effect depends on the wavelength of the incident light, as well as the size of the particle. The contribution of absorbance to the overall LE signal may be significant for particles significantly larger than the wavelength.
There is a simple, approximate relationship between the particle size and the magnitude of the LE signal, ΔVLE. The total light flux incident on the detector, DLE, in the absence of a particle in the OSZ is proportional to the area of illumination, A0. This is approximated byA0≈2aw  (1)Assuming that the intensity of the beam incident on the flow channel 10 is uniform along both its width, a, and over the thickness, 2w, of the beam (i.e. assumed to have a rectangular, rather than gaussian, profile).
If one makes the additional simplifying assumption that a particle completely blocks the light that impinges on it (i.e. perfect, 100% extinction), then the fraction of incident light blocked by the particle is given by ΔA/A0, where ΔA represents the cross-sectional area of the particle. The pulse height, ΔVLE, of the light-extinction signal for particle diameters <2w can then be expressed byΔVLE=(ΔA/A0)V0  (2)
For simplicity, the particles are assumed to be spherical and homogeneous, in order to avoid complicating details related to particle shape and orientation. Quantity ΔA for a particle of diameter d is therefore given byΔA=πd2/4  (3)
In cases where the particle blocks less than 100% of the light incident on it—e.g. where the dominant mechanism for extinction is mostly light scattering, rather than refraction and reflection—quantity ΔA represents the “effective” cross-sectional area, smaller than the actual physical area.
The velocity, v, of the particles that pass through the OSZ is given byv=F/ab  (4)
The pulse width, Δt, represents the time of transit of the particle through the OSZ—i.e. between the 1/e2 intensity points that define the width, 2w. Neglecting the size of the particle compared to quantity 2w, the pulse width is given byΔt=2w/v  (5)
It is instructive to calculate the values of the parameters above for a typical LE sensor—the Model LE400-1E sensor (Particle Sizing Systems, Santa Barbara, Calif.), with a=400 μm, b=1000 μm, and 2w≈35 μm, assuming F=60 ml/min.A0=1.4×104 μm2v=250 cm/secΔt=14×10−6 sec=14 μsec
The smallest particle diameter that typically can be reliably detected (i.e. where ΔVLE exceeds the typical r.m.s. noise level by at least a 2:1 ratio) is approximately 1.3 μm. This corresponds to a physical blockage ratio, ΔA/A0, of 0.000095, or less than 0.01%.
Increasing the intensity of the light source should, in theory, have no influence on the sensitivity, or lower particle size limit, of an extinction-type sensor. For a given baseline voltage, V0, the pulse height, ΔVLE, depends only on the fraction of the illuminated detector area effectively blocked by the particle, ΔA/A0. (The effect of sample turbidity is discussed later.) Only if a more powerful light source possesses lower noise, will the sensor be able to detect reliably a smaller fractional change in effective blocked area, and therefore a smaller particle diameter. However, any such improvement in performance, due to increased S/N ratio, represents only a second-order effect and is usually not significant.
Using the parameters for the LE-type sensor discussed above, one obtains an estimate of the effective volume, VOSZ, of the OSZ,VOSZ=2abw=1.4×107 μm3=1.4×10−5 cm3  (6)
The reciprocal of the OSZ volume, 1/VOSZ, equals the number of “view volumes” contained in 1 cm3 (i.e. 1 ml) of fluid—i.e. 1/VOSZ≈7×104 for the example above.
The quantity 1/VOSZ provides a measure of the “coincidence limit” of the sensor—the concentration (# particles/ml) at which the particles pass one at a time through the OSZ, provided they are spaced uniformly throughout the fluid, with each particle effectively occupying one view volume at any given time. In reality, of course, the particles are located randomly throughout the fluid. Therefore, the particle concentration must be reduced substantially with respect to this “ideal” value—i.e. by 10:1 or more—in order to ensure the presence of only one particle at a time in the OSZ. The actual coincidence limit of the sensor is usually defined as the concentration at which only 1% of the particle counts are associated with two or more particles passing through the OSZ at the same time, possibly giving rise to a single detected pulse of exaggerated pulse height. Hence, the useful coincidence limit of the sensor is typically only 10% (or less) of the value 1/VOSZ. Using the example above, this implies a coincidence concentration of approximately 7,000 particles/ml. In practice the coincidence limit of a sensor of given design will also be a function of particle size. The value indicated is appropriate in the case of very fine particles, having diameters much smaller than the effective thickness, 2w, of the OSZ. The coincidence limit may be significantly lower in the case of particles comparable in size to, or larger than, parameter 2w. Therefore, in practice one often chooses to collect data at a particle concentration of only 50% (or less) of the value given above, in order to eliminate erroneous particle “counts” and distortion of the resulting particle size distribution (PSD).
For applications involving concentrated suspensions and dispersions, it is very desirable to increase the coincidence concentration of the sensor, so that less extensive dilution of the starting sample is required. First, this improvement lowers the volume of clean fluid needed to dilute the sample and reduces the extent to which the diluent fluid must be free of particle contamination. Second, and more important, extensive dilution of the starting concentrated suspension may not be feasible, if it results in significant changes in the PSD—e.g. due to promotion of particle agglomeration. Examples include pH-sensitive oxide “slurries” used for processing semiconductor wafers by the method known as chemical mechanical planarization (CMP). Also, for a variety of applications it is useful, if not essential, to increase the sensitivity of the SPOS method—i.e. to reduce the minimum detectable particle size. Increases in the coincidence concentration and improvements in the sensitivity of LE-type sensors are usually related, and there are several ways in which improvements in both parameters can be achieved.
The most obvious way in which the sensitivity of an extinction-type sensor can be improved is to decrease the cross-sectional area of illumination, A0. Using the example above, this is accomplished by decreasing the lateral cell dimension, a, or the incident beam thickness, 2w, or both. Concerning the latter course of action, the effective thickness, 2w, of the OSZ can be reduced only to a limited extent. This limitation is imposed by the relationship between the focal length of the focusing lens, the depth of the flow cell, and the width of the starting light beam. Given the nature of gaussian beam optics and the limitations imposed by diffraction, it is impractical to decrease parameter 2w below approximately 5 μm. This reduction represents only a 7-fold improvement over the 35-μm value assumed in the example above. Furthermore, in order to achieve relatively high size resolution for smaller particles, it is useful to retain the quadratic dependence of the light-extinction pulse height, ΔVLE, on the particle diameter, d, which obtains only for values of d (substantially) smaller than 2w. Hence, in order to achieve optimal performance for many important applications, it is usually not desirable to make the thickness of the OSZ appreciably thinner than about 10 μm.
Instead, it appears to be more attractive to reduce the lateral dimension, a, of the OSZ—e.g. from 400 μm (using the example above) to 40 μm. To a first approximation (ignoring nonlinear signal/noise effects), this 10-fold reduction in A0 results in a similar 10-fold reduction in the effective cross-sectional area, ΔALE, required to achieve a given fraction of blocked area, ΔALE/A0.
There is a second significant advantage that results from this 10-fold reduction of the width of the flow channel 10. The volume of the OSZ (Equation 6) is also reduced 10-fold, resulting in a reduction of the coincidence concentration by the same factor. Hence, the working sample concentration can be increased 10-fold, permitting a 10-fold lower extent of dilution required for the starting concentrated particle dispersion. Of course, the same 10-fold increase in the coincidence concentration can be achieved through a 10-fold reduction in the cell depth, b, rather than the cell width, a, considered above. However, the improvement in sensor sensitivity would no longer be obtained. Clearly, while dimensions “a” and “b” play equivalent roles with respect to determining VOSZ, and therefore the coincidence concentration, they are not equivalent with respect to influencing sensor sensitivity.
Unfortunately, there is a serious disadvantage to this proposed approach. It is not practical to reduce dimension a (or b, for that matter) to such an extent (i.e. significantly smaller than 100 μm) for reasons that are obvious to anyone familiar with the use of SPOS technology. Such a small dimension virtually invites clogging of the flow channel 10, due to the inevitable existence of contaminant (“dirt”) particles in the diluent fluid and/or large particles associated with the sample, such as over-size “outliers” and agglomerates of smaller “primary” particles. Generally, the minimum lateral dimension (either a or b) of the flow channel 10 in an LE-type sensor should be at least two, and preferably three to four, times larger than the largest particle expected to occur in the sample of interest. Otherwise, frequent clogging of the flow cell is inevitable, thus negating one of the principal advantages of the SPOS technique over an alternative single-particle sensing technique known as “electro-zone,” or “resistive-pore,” sensing (e.g. the “Coulter counter,” manufactured by Beckman-Coulter Inc, Hialeah, Fla.).
One of the previously established ways of increasing the sensitivity of a conventional SPOS-type sensor is to use the method of light scattering (LS), rather than light extinction. With the LS technique the background, or baseline, signal is ideally zero in the absence of a particle in the OSZ. (In reality, there is always some low-level noise due to scattering from contaminants and solvent molecules, plus contributions from the light source, detector and amplifier.) Therefore, the height of the detected signal pulse due to a particle passing through the OSZ can be increased, for a given particle size and composition, simply by increasing the intensity of the light source. This simple expedient has resulted in sensors that can detect individual particles as small as 0.2 μm or smaller.
Fortunately, by adopting a completely different measurement approach, significantly higher sensitivity and coincidence concentration can be achieved from an SPOS device than is provided by a conventional LE or LS sensor. The resulting new apparatus and method form the basis of the present invention. The most significant difference in the optical design of the new sensor concerns the light beam that is used to define the OSZ. Rather than resembling a thin “ribbon” of light that extends across the entire flow channel (i.e. in the x–y plane, FIG. 1), it now consists of a thin “pencil” of light (aligned with the y-axis) that probes a narrow region of the flow channel 10. This beam, typically having an approximately gaussian intensity profile and circular cross section, effectively illuminates only a small fraction of the particles that flow through the sensor. The resulting area of illumination, A0, is much smaller than the value typically found in a conventional sensor, which requires that the beam span the entire width (x-axis) of the flow channel 10. By definition, the intensity of the new beam is highly non-uniform in both the lateral (x-axis) direction and the direction of particle flow (z-axis).
Consequently, particles that pass through the sensor are necessarily exposed to different levels of maximum light intensity (i.e. at z=0), depending on their trajectories. The resulting signal pulse height generated by a particle now depends not only on its size, but also its path through the flow channel 10. Particles that pass through the center of the illuminating beam, where the intensity is highest, will generate LE (or LS) pulses of maximum height for a given size, while those that pass through regions of lesser intensity will produce pulses of corresponding reduced height. Hence, the use of a beam of non-uniform (usually, but not necessarily gaussian) intensity profile gives rise to the so-called “trajectory ambiguity” problem. A number of researchers have attempted to address this problem, using a variety of approaches.
The problem of trajectory ambiguity in the case of remote in-situ measurement of scattered light signals produced by unconfined particles was discussed more than twenty years ago by D. J. Holve and S. A. Self, in Applied Optics, Vol. 18, No. 10, pp. 1632–1652 (1979), and by D. J. Holve, in J. Energy, Vol. 4, No. 4, pp. 176–183 (1980). A mathematical deconvolution scheme, based on a non-negative least-squares (NNLS) procedure, was used to “invert” the set of measured light scattering pulse heights produced by combustion particles moving in free space. The measurement volume was defined by a ribbon (elliptical) beam with a gaussian intensity profile and an off-axis distant pinhole and detector, reverse imaged onto the beam. Holve et al explicitly rejected the well-known method of matrix inversion, as it was said to be ineffective when applied to their typical light scattering data. From the results and explanation provided, it is apparent that the resolution and accuracy of the PSDs that could be obtained using their light scattering scheme and NNLS deconvolution procedure were relatively poor. Multimodal distributions required relatively widely spaced particle size populations in order to be resolved reasonably “cleanly” using the referenced apparatus and method.
As disclosed in the Holve articles, the measurement region from which the scattered light signal is detected originates from a portion of the cross section of the illuminating beam. As will be discussed, the present invention also utilizes a beam that is spatially non-uniform in intensity, preferable having a circular gaussian profile. However, the present invention fully “embraces” this non-uniformity. That is, the measurement zone encompasses the entire cross section of the beam and not just the central region of highest (and least-variable) intensity. The particles to be counted and sized are caused to flow uniformly through a confined, well-defined space (flow channel) where the fraction of particles of any given size that is measured is fixed and ultimately known. The region from which data are collected is similarly fixed and well-defined and relatively immune to vibrations and optical misalignment. Given the inherent stability and different nature of the physical design associated with the present invention, it should not be surprising that the PSD results possess not only high sensitivity but also superior, unprecedented particle size resolution compared to the results obtained from the Holve approach. It is observed also that Holve's system is necessarily confined to light scattering as the means of detection. By contrast, the novel apparatus and methods taught in the present invention make possible sensors that are equally effective based on light scattering or light extinction.
Partly because of the limited quality of the PSD results that could be achieved using the apparatus and method described by Holve et al, there was subsequent recognition of the need to develop alternative methods that would permit gaussian beams to be used effectively for particle size determination. Of course, the simplest remedy, if appropriate, was seen to be elimination of the gaussian beam, itself, that is the source of the problem. Foxyag, in U.S. Pat No. 3,851,169 (1974), proposed altering the intensity distribution of the laser beam, in order to reduce the non-uniformity inherent in its gaussian profile. Separately, G. Grehan and G. Gouesbet, in Appl. Optics, Vol 25, No. 19, pp 3527–3537 (1986), described the use of an “anti-gaussian” correcting filter in an expanded beam before focusing, thereby producing a “top-hat” beam profile, having substantially uniform intensity over an extended region. Fujimori et al, in U.S. Pat. No. 5,316,983 (1994), used a “soft” filter to convert a gaussian laser beam into a flattened intensity distribution.
Other proposals involved physically confining the flowing particles, so that they are forced to pass through the central portion of the laser beam, where the intensity is substantially uniform. An example is described by J. Heyder, in J. Aerosol Science, Vol 2, p. 341 (1971). This approach was also adopted by Bowen, et al, in U.S. Pat. No. 4,850,707 (1989), using a focused elliptical laser beam with a gaussian intensity profile, with a major axis much longer than the width of a hydrodynamically-focused “channel” containing the flowing particles. All of the particles are therefore exposed to substantially the same maximum intensity as they flow through the beam.
An early proposal for accommodating gaussian beams, proposed by Hodkinson, in Appl. Optics, Vol. 5, p. 839 (1966), and by Gravitt, in U.S. Pat. No. 3,835,315 (1974), was to determine the ratio of the peak scattered intensity signals detected simultaneously at two different scattering angles. This ratio is ideally independent of the intensity incident on the particle and, according to Mie theory, is uniquely related to its size. The reliability of this method was improved using the proposal of Hirleman, Jr., et al, in U.S. Pat. No. 4,188,121 (1980). The peak scattered intensities at more than two scattering angles are measured and the ratios of all pairs of values calculated. These ratios are compared with calibration curves in order to establish the particle diameter.
Several methods were suggested for selecting only those particles that have passed substantially through the center of the gaussian beam. A scheme for collecting off-axis scattered light from a distant, in-situ measurement volume, similar to the apparatus used by Holve et al, was described by J. R. Fincke, et al, in J. Phys. E: Sci. Instrum., Vol 21, pp. 367–370 (1988). A beam splitter is used to distribute the scattered light between two detectors, each having its own pinhole aperture. One of the apertures is smaller than the beam waist in the measurement volume. Its detector is used to “select” particles suitable for measurement by the second detector, having a considerably larger aperture, ensuring that they pass substantially through the center of the beam, and therefore are eligible for counting and sizing. Notwithstanding the simplicity and apparent attractiveness of this approach, it was ultimately rejected by the authors, because of the difficulty of maintaining precise, stable alignment of the various optical elements. (This rejection is not unrelated to the limited quality of the PSD results obtained by Holve et al, alluded to above.)
Another set of proposed methods suggested the use of two concentric laser beams of different diameters, focused to a common region, through which particles are allowed to transversely flow, with the outside beam significantly larger in diameter than the inner beam. Two detectors are used to measure the amplitudes of light signals scattered by particles passing through each respective beam, distinguished by different wavelength (color) or polarization. Only those particles that pass through the central portion of the larger measurement beam, where the intensity is substantially uniform, produce signals from the smaller “validating” beam. Schemes using beams of two different colors are described by Goulas, et al, in U.S. Pat. No. 4,348,111 (1982), and Adrian, in U.S. Pat. No. 4,387,993 (1983). A variation on the concentric two-beam method is described by Bachalo, in U.S. Pat. No. 4,854,705 (1989). A mathematical formulation is used to process the two independently measured signal amplitudes together with the known beam diameters and intensities to determine the particle trajectory and, ultimately, the particle size. A variation on this approach is described by Knollenberg, in U.S. Pat. No. 4,636,075 (1987), using two focused, concentric beams distinguished by polarization. An elongated, elliptical beam shape is used to reduce the ratio of beam diameters needed to achieve acceptable particle size resolution and higher concentration limits.
Yet another variation of the two-beam approach is described by Flinsenberg, et al, in U.S. Pat. No. 4,444,500 (1984). A broad “measuring” beam and a narrower “validating” beam are again utilized, but in this case the latter is located outside the former, allowing both beams to have the same color and polarization. The plane containing the axes of the two beams is aligned parallel to the flow velocity of the particles. Achieving coincidence of two scattering signals detected separately from each beam ensures that the only particles to be counted and sized are those that have traversed the narrow beam, and hence the central region of the broad, measuring beam. Still another variation of the two-beam approach is described by Hirleman, Jr., in U.S. Pat. No. 4,251,733 (1981). Through the use of two physically separated gaussian beams, the particle trajectory can be determined from the relative magnitudes of the two scattered light signal pulses. This, in turn, permits the intensity incident on the particle everywhere along its trajectory to be calculated, from which the particle size can be determined.
Other proposals take advantage of an interferometric technique commonly utilized in laser Doppler velocimetry—i.e. crossing two coherent laser beams to obtain a fixed fringe pattern in a spatially localized region. The particle size can be determined from the peak scattering intensity, provided differences in trajectory can be accounted or compensated for. A straightforward scheme was proposed by Erdmann, et al, in U.S. Pat. No. 4,179,218 (1979), recognizing that a series of scattered light pulses is produced by each particle, related to the number of fringes through which it passes. The number of pulses establishes how close the particle has approached the center of the “probe” volume established by the fringe pattern, where the number of fringes is greatest and the intensity is brightest, corresponding to the center of each gaussian beam. An alternative method was proposed by C. F. Hess, in Appl. Optics, Vol. 23, No. 23, pp. 4375–4382 (1984), and in U.S. Pat. No. 4,537,507 (1985). In one embodiment, two coherent beams of unequal size are crossed, forming a fringe pattern. The small beam “identifies” the central region of the larger beam, having substantially uniform (maximal) intensity. A signal that contains the maximum a.c. modulation indicates that the particle has passed through the center of the fringe pattern and, hence, the middle of the large beam. The particle size is extracted from the “pedestal” (d.c.) signal after low-pass filtering removes the a.c. component. In a second embodiment, two crossed laser beams of one color are used to establish a fringe pattern at the center of a third, larger beam of a second color. A first detector establishes from the magnitude of the a.c. component of the scattered light signal whether a particle has passed substantially through the center of the fringe pattern. If so, the pulse height of the scattered light produced by the large beam, obtained from a second detector, is recorded. Bachalo, in U.S. Pat. No. 4,329,054 (1982), proposed distinguishing the central portion of a fringe pattern, corresponding to the central region of each gaussian beam, by using an additional small “pointer” beam of different color or polarization, responding to a separate detector means.
Finally, assorted other techniques have been proposed for addressing the gaussian beam/trajectory ambiguity problem. Bonin, et al, in U.S. Pat. No. 5,943,130 (1999), described a method for rapidly scanning a focused laser beam through a measurement volume, resulting in a scattered intensity pulse each time the beam crosses a particle. Given the high scanning frequency and velocity and the relatively low particle velocity, each particle is scanned several times while it is in the measurement volume. The resulting series of pulses can be fitted to the beam intensity profile and the maximum of the gaussian fit mapped to a particle diameter using a calibrated response function that correlates particle size with scattered light intensity. DeFreez, et al, in U.S. Pat. No. 6,111,642 (2000), proposed a “flow aperturing” technique. A particle/fluid delivery nozzle is designed so that the lateral velocity profile of the emerging particles approximately matches the gaussian intensity profile of the laser beam. The reduction in incident light level due to increasing distance of the particle trajectory from the beam axis is compensated approximately by the increase in integration time of the scattering signal, due to the lower velocity. The net integrated scattering signal is therefore ideally independent of the trajectory. An improvement was proposed by Girvin, et al, in U.S. Pat. No. 6,016,194 (2000), using a linear detector array to individually detect the scattered light signals associated with substantially each particle trajectory. The gain of each detector element can be adjusted to compensate for variations that remain in the net signal response of the system in the lateral direction, due to incomplete matching of the nozzle velocity and laser beam intensity profiles, differences in individual detector efficiencies and other effects.